A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions

被引：17
作者：
Zheng, Rumeng [1 ]
Liu, Fawang [2 ,3 ]
Jiang, Xiaoyun [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia
[3] Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350116, Fujian, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2020年 / 104卷
基金：
澳大利亚研究理事会; 中国国家自然科学基金;
关键词：
Legendre spectral method; L1 method on graded meshes; Two-dimensional multi-term time-fractional diffusion equation; Stability and convergence; Fast algorithm; Non-smooth solutions; FINITE-ELEMENT-METHOD; NUMERICAL-METHODS; WAVE EQUATION; APPROXIMATION;
D O I：
10.1016/j.aml.2020.106247
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a Legendre spectral method on graded meshes for solving the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions. The L1 method on graded meshes is developed in temporal direction. In the spatial direction, we choose the Legendre spectral method. With the help of mathematical induction method, the stability and convergence of the above mentioned method are theoretically proved. To improve the computational efficiency, we use the fast algorithm in the numerical implementation. Some numerical results are provided to verify the theoretical analysis and demonstrate the effectiveness of our method. (C) 2020 Elsevier Ltd. All rights reserved.
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页数：8
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